Wizard multiclass

[wunderkid]

This is probably an incredibly dense question that has a very simple answer.

But. The wizards spell book, say I am a wizard 3/bard 10.

And I come across a wizards spell book. Can I copy a 5th level wizard spell into the book and prepare it using the rules for wizard?

As far as I can remember the multiclass rules don't prevent this and neither does the wizard preparation. But I don't have the book to hand so if anyone can cite for me I'd appreciate it.

[Segev]

The rules are a little bit confusing, because of the way the Wizard single-class rules for preparing spells are written, which say "as long as you have a spell slot of the appropriate level." However, the correct, non-broken reading of the RAW for multiclassing spellcasters is that you prepare the spells for each class as if you were only a member of that class of your level in that class. Thus, you prepare only spells that a 3rd level wizard could prepare, despite having spell slots of a 13th level wizard (or bard). Likewise, you can only learn Bard spells that a 10th level Bard could learn, when you level up to Bard 10.

Otherwise, Wizard 17/Cleric 1/Druid 1/Sorcerer 1 would have 9th level spell access to all three lists.